Saturday, June 26, 2010

So I self-promoted my "Self-Promotion" comic because I wanted to either be ironic or be whatever it is that people call "ironic" but really isn't but makes English teachers rip their hair out.

I expected downvotes and negative reviews and comments from those that saw the URL and the user id of the poster (both containing "xwhy" in them) without clicking on the link to see that that was part of the joke. The jokes back on me.

The results: 260+ views on Stumbleupon, with no comments and no one listed as liking it; 150 visits from reddit, with 4 up votes and 3 down votes, and no comments; and no one saw it on digg, except me.

On the other hand, David Morgan-Mar posted a link on his Facebook page. Over 700 hits, 11 people liked it, with two comments.

Self-promoting doesn't pay. Especially when you have a small, select audience to begin with. I'm happy to have you.

Thursday, June 17, 2010

The character, 'Leven Hex, dates back to April 2008, but I held off because I had just done a comic book strip at the end of March, and I ran hex-based 0'Factor instead. And then I never got around to doing this one. Things happen.

I spent a lot more time on this one than I had expected to. And I probably could've spent even more, but I had to finally let it go. And then I updated it again this morning because I thought it was too tall and there was a lot of empty, blue sky. And I still didn't get around to adding any grass by the pond, or mixing any green in the water.

If you're curious, I looked through a lot of covers to find the right look.

But suppose instead of three consecutive numbers, we had five consecutive numbers, which were split with the three smaller values on the left and the two greater values on the right? That would give us:

a2 + b2 + c2 = d2 + e2

The answer is in the previous post. I'll omit it here in case you want to work it out.

Now, a couple approaches could work here. The first, and probably best if you plan on going further, is to replace the variables with n, n+1, n+2, etc., and then using FOIL (or a "FOIL"-free alternative if you hate "FOIL"), combining like terms and solving the resulting equation.

The other, which I can use on Day 1, is guess and check. Okay, stop laughing and rolling your eyes, and hear me out.

First of all, most of my students haven't handled a scientific calculator very much let alone a TI-83, 84, or N-Spire. (Yes, we had a bunch donated to the school as part of a technology initiative. Unfortunately, they aren't allowed to be used during the Regents exams, so we have to switch back to the older calculators. But that's a rant for another day.) An activity like this could be a simple and thoughtful first exercise.

Second, many of them have little or no Number Sense or Estimating skills. How would they approach the problem? Would they try 3, 4, 5, 6, 7 first? When that doesn't work, will they move to 4, 5, 6, 7, 8, or will they jump a little higher a little faster? But if they don't try every combination, how will they know if they went too far and passed the answer?

Then, after finding the answer and comparing it to 3, 4, 5, what would their first guess be for

a2 + b2 + c2 + d2 = e2 + f2 + g2 ?

Naturally, all of this occurs to me during the last week of classes, after the final exam has been given.

Tuesday, June 08, 2010

I recently found out that mathematics and science writer, Martin Garnder passed away a couple of weeks ago.

I first discovered Gardner at Xaverian High School, browsing the library shelves, probably looking for a puzzle book. I found a copy of The Incredible Dr. Matrix, which was a fun book to read. Besides being the first place where I ever encountered the Lincoln/Kennedy connections (complete with corrections, such as Lincoln's secretary's name was John, not Kennedy), but it had some great puzzles that got me thinking (a dangerous pasttime).

One problem that I remembered was that Gardner listed

32 + 42 = 52,

which everyone knows, and then added that

102 + 112 + 122 = 132 + 142,

which I had to independently verify.

It hadn't occured to me that this progression might continue. The puzzle was to find four consecutive numbers which, when squared, have the same sum as the sum of the squares of the next three consecutive numbers after that.

Having already had Algebra under my belt by that point, it turned out not to be a problem at all.

My brother, Joseph, saw the book and mentioned that Gardner had puzzles in Asimov's Science Fiction, which he had a subscription to. The one story that comes to mind had this as the basic puzzle:

A family is riding a rocket ship from the Moon to Earth. A child looks out the front window and then runs to the rear window. He then tells his father that the Earth and the Moon appear to be the same size. The puzzle, which included some information that I'd have to look up, was find the position of the spaceship relative to the Earth and Moon.

I haven't read anything by Gardner in quite a while, but I should probably stop by the library and find a book or two of his and see if I can find some good puzzles for my students.

About Me

Mr. Burke is a high school math teacher in New York as well as a part-time writer, and a fan of science-fiction/fantasy books and films.
He started making his own math webcomic totally by accident as a way of amusing his students and trying to make them think just a little bit more.
Unless otherwise stated, all math cartoons and other images on this webpage are the creation and property of Mr. Chris Burke and cannot be reused without permission.
Thank you.